Histogram Questions with Solutions | Practice Problems – Testbook

To understand histograms well, practice is very important. Here, you’ll find questions with answers to help you learn how to read and work with histograms step by step.

In statistics, a histogram is a type of bar graph used to show how often data appears within certain ranges. It’s mostly used for continuous data, meaning numbers that can take any value in a given range.

Unlike regular bar graphs, histograms have no gaps between the bars, showing that the data flows without breaks. This makes them perfect for showing how values are grouped into intervals.

Key Points to Remember About Histograms:

• Histograms are used to display continuous (non-stop) data.
• Bars touch each other—there are no spaces in between.
• The height of each bar shows how many times a value appears (called frequency).
• The width of each bar shows the size of the interval or group.
• Always start your graph from zero, and use equal intervals unless noted.
• If the graph skips some numbers at the beginning, a small zig-zag line is drawn on the axis to show the break.
• When all intervals are the same size, the area of each bar matches the frequency.

Discover more about histograms and how to create one by visiting this page.

Let's dive into some questions related to plotting and interpreting histograms.

Example 1: Data Table

Questions:

1. What is the total number of data points?
2. Which interval has the highest frequency?
3. Which interval has the lowest frequency?

Solution:

1. Total = 8 + 12 + 18 + 7 = 45
2. Highest frequency = 20–30 interval
3. Lowest frequency = 30–40 interval

Example 2: Test Score Distribution

Question: How many students scored 60 or more?
Answer: 8 + 12 = 20 students

Example 3: Frequency Table

Question: What is the cumulative frequency of class 25–35?
Answer : 6 + 11 + 9 = 26

Example 4: Histogram-Based Attendance

Question: How many people are younger than 30?
Answer: 4 + 8 + 15 = 27

Example 5: Employee Salary Ranges

Question: How many employees earn less than ₹25,000?
Answer: 7 + 13 + 10 = 30

Example 6: Height of Boys

Question: Which class has the highest frequency?
Answer: 150–160 (12 boys)

Example 7:Response Time (seconds)

Given data: {15, 20, 22, 24, 28, 32, 34, 36, 38, 40, 42, 45}

Group into class intervals: